Premium
A two‐grid method for characteristic expanded mixed finite element solution of miscible displacement problem
Author(s) -
Hu Hanzhang,
Chen Yanping
Publication year - 2020
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2292
Subject(s) - finite element method , mathematics , displacement (psychology) , mixed finite element method , compressibility , nonlinear system , grid , mathematical analysis , extended finite element method , pressure correction method , mathematical optimization , geometry , mechanics , structural engineering , psychology , physics , quantum mechanics , engineering , psychotherapist
Summary A combined method consisting of mixed finite element method (MFEM) for the pressure equation and expanded mixed finite element method with characteristics(CEMFEM) for the concentration equation is presented to solve the coupled system of incompressible miscible displacement problem. To solve the resulting nonlinear system of equations efficiently, the two‐grid algorithm relegates all of the Newton‐like iterations to grids much coarser than the original one, with no loss in order of accuracy. It is shown that coarse space can be extremely coarse and our algorithm achieve asymptotically optimal approximation when the mesh sizes satisfy H = O ( h1 4) . Numerical experiment is provided to confirm our theoretical results.